describe the long run behavior of f(x)=x^7 as x→−∞, f(x)→? as x→∞, f(x)→? question help: message instructor

Explanation:

Step1: Analyze when $x\to -\infty$

For $y = x^7$, when $x$ is a large - negative number, say $x=-N$ where $N$ is a large positive number. Then $f(-N)=(-N)^7=-N^7$. As $N\to\infty$, $-N^7\to -\infty$. So as $x\to -\infty$, $f(x)\to -\infty$.

Step2: Analyze when $x\to\infty$

When $x$ is a large positive number, say $x = N$ where $N$ is a large positive number. Then $f(N)=N^7$. As $N\to\infty$, $N^7\to\infty$. So as $x\to\infty$, $f(x)\to\infty$.

Answer:

As $x\to -\infty$, $f(x)\to -\infty$; as $x\to\infty$, $f(x)\to\infty$